Russell 2000 monthly returns
Russell 2000 is by far the most common benchmark for mutual funds that identify themselves as "small-cap". Similar to S&P 500, Russell 2000 is a value weighted index and many index funds and exchange-traded funds (e.g. iShares Russell 2000 Index (IWM)) attempt to replicate (before fees and expenses) the performance of the Russell 2000 by holding the same stocks as the index, in the same proportions.
For our purpose, we try to model the monthly returns (and volatility) using econometric techniques
The log monthly returns distribution has small mean (not significantly different from zero), symmetric (skewness is statistically negligible), but heavy tails. Furthermore, the monthly returns are serially correlated and possess an ARCH effect.
Examining the descriptive statistics and the graphs above, GARCH(1,1) may be a good candidate for modeling the time-varying conditional volatility. Initially, we assume a gaussian innovations, fit a model. and examine the residuals for this assumptions. In our prior analysis financial time series case studies, we resorted to a fat-tailed distributed innovations (e.g. Student t-distribution or GED) to absorb the remaing excess kurtosis.